Aircraft: B737
Phase of flight: Initial Approach
Anomaly: Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy

While on approach to ZZZ from the ZZZZZ transition to ZZZZZ1; Approach Control advised us that we were off course. Autopilot was engaged and flight directors were following the magenta course with LNAV - VNAV PATH. We looked and saw that the course had a curve just outside of ZZZZZ1 to intercept instead of proceeding direct to ZZZZZ1. We had no indication in the aircraft that this wasn't normal for the FMS. If I were to guess; I would say that the difference was between .5-1 mile north of ZZZZZ1 with the intercept. The Controller told us to take a look on the ground. I did reprogram the FMS with the arrival and approach in the FMS on the ground; and found nothing out of the ordinary. On descent to ZZZ we were given many different altitude and speeds that were faster and lower than the STAR. I don't know if that had anything to do with it. In summary; we didn't see anything out of the ordinary from a cockpit perspective; but after looking at FlightAware of our flight and the flight after us; we could see a difference in the two. We did talk to the Crew that flew behind us and asked if they were coupled with the autopilot as well to try to figure the difference with the ground track. They were doing the same thing as us; but the software between the aircraft had different outcomes. On the arrival into ZZZ airport from ZZZZZ to ZZZZZ1; Approach informed us that we were off course; said we had flown through the final and gave us a heading to re-intercept. By that time the aircraft was already intercepting the final approach course. Earlier we briefed the arrival; all points checked out and we were flying a magenta line to the above fixes. During the arrival; Approach gave us many altitude and speed changes; along with crossing fixes. Although there were a lot of changes we were able to enter them into the FMS. During the approach and transition the aircraft appeared to us to be on course and profile. When the Controller told us that we were off course and then gave us an intercept heading and altitude; to us it didn't make sense; at the time; the heading given would have had us paralleling the final approach course. The aircraft intercepted the final just outside of ZZZZZ1. To us the approach looked very normal and the information given by the Controller was confusing because it looked like we were flying the proper transition. on the ground I called Dispatch and had him connect me to the ATC desk. I spoke with (ATC Specialist Name) told him what took place and he called TRACON. In (ATC Specialist) email to me he said that they were aware of a profile issue; had many meetings about this; and were trying to get a Jepps update. On the way to the hotel my First Officer found our flight path on Flight Aware and it did show; what looked like; a minor deviation. Like I said earlier; the arrival and approach were properly briefed all points checked out and we were on a magenta line and on profile. We captured final and due to the confusion with ATC I turned off the autopilot and hand flew it the rest of the way. Air Carrier Pilot Crew reported while using the autopilot; ATC informed them the aircraft was off course.